Distributed Estimation of Dynamic Fields over Multi-agent Networks

TL;DR

This paper introduces three novel distributed algorithms for estimating dynamic fields over sensor networks, achieving unbiased, bounded-error estimates using local measurements and neighbor information, validated through extensive simulations.

Contribution

The paper develops three new distributed estimators (PIKF, DIKF, CIKF) that outperform existing methods in dynamic field estimation over multi-agent networks.

Findings

All three estimators achieve unbiased estimates with bounded MSE.

The proposed methods outperform existing solutions in numerical evaluations.

Trade-offs between the estimators are characterized and analyzed.

Abstract

This work presents distributed algorithms for estimation of time-varying random fields over multi-agent/sensor networks. A network of sensors makes sparse and noisy local measurements of the dynamic field. Each sensor aims to obtain unbiased distributed estimates of the entire field with bounded mean-squared error (MSE) based on its own local observations and its neighbors' estimates. This work develops three novel distributed estimators: Pseudo-Innovations Kalman Filter (PIKF), Distributed Information Kalman Filter (DIKF) and Consensus+Innovations Kalman Filter (CIKF). We design the gain matrices such that the estimators achieve unbiased estimates with bounded MSE under minimal assumptions on the local observation and network communication models. This work establishes trade-offs between these three distributed estimators and demonstrates how they outperform existing solutions. We validate our results through extensive numerical evaluations.